Abstract: Over the past decade, the availability of astrophysical data collected by electromagnetic observatories and gravitational-wave (GW) interferometers, supplemented by the information obtained from Earth-based laboratory experiments, has opened a new era for the investigation of neutron star structure and dynamics. Besides being a valuable source of information on the Equation of State (EOS) of matter in the star interior, the new data provide an unprecedented opportunity to constrain the underlying models of nuclear dynamics at supranuclear density.  he Bayesian approach has been recently employed to explore the possibility to constrain repulsive three-nucleon (NNN) forces—which are known to play the leading role in determining the stiffness of the EOS at high density—using both available and mock data.  The results of these studies suggest that a single neutron star merger event observed by a third-generation GW interferometer, such as the Einstein Telescope or Cosmic Explorer, may allow to pin down the strength of the repulsive NNN potential with remarkable accuracy.